• Title/Summary/Keyword: Bartle integral

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GENERALIZED FUZZY NUMBER VALUED BARTLE INTEGRALS

  • Park, Chun-Kee
    • Communications of the Korean Mathematical Society
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    • v.25 no.1
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    • pp.37-49
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    • 2010
  • In this paper we introduce the integration of scalar valued functions with respect to a generalized fuzzy number measure which we call the generalized fuzzy number valued Bartle integral. We first establish some properties of the generalized fuzzy number measures and then study the generalized fuzzy number valued Bartle integrals.

THE BARTLE INTEGRAL AND THE CONDITIONAL WIENER INTEGRAL ON C[0,t]

  • Ryu, Kun-Sik;Im, Man-Kyu
    • Communications of the Korean Mathematical Society
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    • v.19 no.4
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    • pp.643-660
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    • 2004
  • In this paper, we give a new formula between the conditional Wiener integral E(F|X), the conditional Wiener integral of F given X, and the integral with respect to a measure-valued measure, a kind of Bartle integral. Using this formula, we give some examples of evaluation of E(F|X).

INTEGRATION WITH RESPECT TO ANALOGUE OF WIENER MEASURE OVER PATHS IN WIENER SPACE AND ITS APPLICATIONS

  • Ryu, Kun-Sik
    • Bulletin of the Korean Mathematical Society
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    • v.47 no.1
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    • pp.131-149
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    • 2010
  • In 1992, the author introduced the definition and the properties of Wiener measure over paths in Wiener space and this measure was investigated extensively by some mathematicians. In 2002, the author and Dr. Im presented an article for analogue of Wiener measure and its applications which is the generalized theory of Wiener measure theory. In this note, we will derive the analogue of Wiener measure over paths in Wiener space and establish two integration formulae, one is similar to the Wiener integration formula and another is similar to simple formula for conditional Wiener integral. Furthermore, we will give some examples for our formulae.